First-order gradients of skew rays of axis-symmetrical optical systems
JOSA A, Vol. 24, Issue 3, pp. 776-784 (2007)
http://dx.doi.org/10.1364/JOSAA.24.000776
Enhanced HTML 
Acrobat PDF (154 KB)
Abstract
Current commercial software for analysis and design of optical systems use finite difference (FD) approximation methodology to estimate the gradient matrix of a ray with respect to system variables. However, FD estimates are intrinsically inaccurate, subject to gross error when the denominator is excessively small relative to the numerator. We avoid these problems and determine these gradients by the application of Snell’s law. We give the background and basics for determining the first-order gradients of skew rays of optical systems, whereby the differential vector of any ray can be estimated by the product of the developed gradient matrix and differential changes of system variables. The most important application is for optical design by use of optimization methods where the merit function is defined as the spot size. FD used for such optimization is slow for large systems and subject to inaccuracy. The presented methodology is shown to be accurate and computationally faster than traditional FD. Two illustrative examples are provided to validate the proposed method.
© 2007 Optical Society of America
OCIS Codes
(080.2730) Geometric optics : Matrix methods in paraxial optics
(080.2740) Geometric optics : Geometric optical design
(080.3620) Geometric optics : Lens system design
(220.4830) Optical design and fabrication : Systems design
ToC Category:
Geometric Optics
History
Original Manuscript: June 29, 2006
Manuscript Accepted: September 22, 2006
Published: February 14, 2007
Citation
Psang Dain Lin and Chuang-Yu Tsai, "First-order gradients of skew rays of axis-symmetrical optical systems," J. Opt. Soc. Am. A 24, 776-784 (2007)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-3-776
You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.
Contact your librarian or system administrator
or
Log in to access OSA Member Subscription
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.
Contact your librarian or system administrator
or
Log in to access OSA Member Subscription
You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.
Contact your librarian or system administrator
or
Log in to access OSA Member Subscription
You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.
Contact your librarian or system administrator
or
Log in to access OSA Member Subscription
Related Journal Articles 
- Computational study of diffraction patterns for near-field Fresnel and Gabor zone plates (JOSAA)
- FOCOIVA Lens: A Scanner in the Lateral and Longitudinal Directions (AO)
- One-Radius Triplets (AO)
- Modification of the formulas for third-order aberration coefficients (JOSAA)
- Design of spherically corrected, achromatic variable-focus liquid lenses (OE)
Related Conference Papers
- Twenty-First Century Optical Tolerancing: A Look at the Past and Improvements for the Future
- Nonanamorphic imaging with three conic mirrors
- The research for uniform illumination aystems
- Intersection measurement with CCD in detecting multi-targets
- Design of complex optical system for measuring vibrant track of cable crossing river
« Previous Article | Next Article »
OSA is a member of 